Estimation of Spectra of High-dimensional Separable Covariance Matrices

Debashis Paul (University of California, Davis)

We consider the problem of estimating the joint spectra of high-dimensional time series for which the observed data matrix is assumed to have a separable covariance structure. The primary interest is in estimating the distribution of the eigenvalues of the marginal covariance of the observation vectors, under partial information -- such as stationarity or sparsity -- on the temporal covariance structure. We develop a method that utilizes random matrix theory to estimate the unknown population spectra by repressing the spectrum of the dimensional covariance matrix on a simplex. We prove the consistency of the proposed estimator under the dimension proportional to the sample size setting. Furthermore, we develop a resampling-based method for statistical inference on low-dimensional functionals of the joint spectrum of the population covariance matrix.

This is a joint work with Lili Wang (Zhejiang Gongshang University).


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